"The only, and essential, characteristics of parody are, on the one hand, to evoke an existing work while being noticeably different from it and, on the other, to constitute an expression of humour or mockery," the EU rules state.

Since when does mockery have to be funny? Political cartoons are usually mocking somebody or something but rarely laugh-producing. I hope they mean that a judge would rule on whether the parody was either funny OR mocking.

There are two distinct types of parody - one is mocking the song itself - Billy Connolly's D.I.V.O.R.C.E being the classic example; the other is just when you use a song that is familiar to people to get over a point, humorous or otherwise.

Yeah, Acorn, I guess so. But I do not consider a song a "parody" just because it uses new lyrics to an older melody. If you "use a song that is familiar to people to get over a point, humorous or otherwise," you have to incorporate a good deal of the lyrics to the original song (albeit often slightly modified) for it to be a parody.